Review of Decoherence Free Subspaces, Noiseless Subsystems, and Dynamical Decoupling

Abstract

Quantum information requires protection from the adverse affects of decoherence and noise. This review provides an introduction to the theory of decoherence-free subspaces, noiseless subsystems, and dynamical decoupling. It addresses quantum information preservation as well protected computation.

34 pages, 4 figures. Based on lecture notes from a course on quantum error correction given by the author at USC in Spring 2007 and Fall 2011, 2013. Prepared for a special issue of Adv. Chem. Phys. on Quantum Information and Computation for Chemistry. v3: some parts rewritten for clarity, various corrections

References in corpus (10)

• Performance of Deterministic Dynamical Decoupling Schemes: Concatenated and Periodic Pulse Sequences
• Optimal Dynamical Decoherence Control of a Qubit
• High fidelity quantum gates via dynamical decoupling
• Towards Fault Tolerant Adiabatic Quantum Computation
• Preserving qubit coherence by dynamical decoupling
• Performance comparison of dynamical decoupling sequences for a qubit in a rapidly fluctuating spin-bath
• Local observation of antibunching in a trapped Fermi gas
• Protection of quantum systems by nested dynamical decoupling
• Enhanced Convergence and Robust Performance of Randomized Dynamical Decoupling
• Rigorous Performance Bounds for Quadratic and Nested Dynamical Decoupling

Cited by in corpus (122)

• The theory of variational hybrid quantum-classical algorithms
• Noisy intermediate-scale quantum (NISQ) algorithms
• Quantum Coherence as a Resource
• Quantum computational chemistry
• Quantum Error Mitigation
• Theory of variational quantum simulation
• Decoherence-free interaction between giant atoms in waveguide QED
• Gate count estimates for performing quantum chemistry on small quantum computers
• Quantum computing enhanced computational catalysis
• Variational quantum simulation of general processes
• Demonstration of fidelity improvement using dynamical decoupling with superconducting qubits
• A quantum algorithm for evolving open quantum dynamics on quantum computing devices
• Quantum Machine Learning for Chemistry and Physics
• Quantum Simulation of Helium Hydride in a Solid-State Spin Register
• Experimental noise filtering by quantum control
• Time-Dependent Density Matrix Renormalization Group Algorithms for Nearly Exact Absorption and Fluorescence Spectra of Molecular Aggregates at Both Zero and Finite Temperature
• Exploiting locality in quantum computation for quantum chemistry
• Orbital entanglement in quantum chemistry
• Quantum Simulation of Quantum Field Theory in the Light-Front Formulation
• Manipulating Optical Nonlinearities of Molecular Polaritons by Delocalization
• Quantum-optimal-control-inspired ansatz for variational quantum algorithms
• Prospects for Quantum Computing with an Array of Ultracold Polar Paramagnetic Molecules
• Protected ultrastrong coupling regime of the two-photon quantum Rabi model with trapped ions
• Quantum algorithm for calculating molecular vibronic spectra
• Automatic spin-chain learning to explore the quantum speed limit
• A general quantum algorithm for open quantum dynamics demonstrated with the Fenna-Matthews-Olson complex
• Crosstalk Suppression for Fault-tolerant Quantum Error Correction with Trapped Ions
• WavePacket: A Matlab package for numerical quantum dynamics. I: Closed quantum systems and discrete variable representations
• Quantum Phase Estimation with Time-Frequency Qudits in a Single Photon
• Spectroscopy of cross-correlations of environmental noises with two qubits
• Geometric formalism for constructing arbitrary single-qubit dynamically corrected gates
• Benchmarking of Different Optimizers in the Variational Quantum Algorithms for Applications in Quantum Chemistry
• Quantum natural gradient generalised to noisy and non-unitary circuits
• Hardware-Encoding Grid States in a Non-Reciprocal Superconducting Circuit
• Training and Classification using a Restricted Boltzmann Machine on the D-Wave 2000Q
• Error-robust quantum logic optimization using a cloud quantum computer interface
• Quantum Computing: An Overview Across the System Stack
• Simulating Open Quantum System Dynamics on NISQ Computers with Generalized Quantum Master Equations
• To freeze or not to: Quantum correlations under local decoherence
• Dephasing of Transverse Spin Current in Ferrimagnetic Alloys
• Demonstrating Bayesian Quantum Phase Estimation with Quantum Error Detection
• WavePacket: A Matlab package for numerical quantum dynamics. II: Open quantum systems, optimal control, and model reduction
• Implementation-independent sufficient condition of the Knill-Laflamme type for the autonomous protection of logical qudits by strong engineered dissipation
• Hybrid quantum-classical neural network for calculating ground state energies of molecules
• Quantum simulation of three-body interactions in weakly driven quantum systems
• From Symmetries to Commutant Algebras in Standard Hamiltonians
• A quadrupolar exchange-only spin qubit
• Backaction driven, robust, steady-state long-distance qubit entanglement over lossy channels
• Universally Robust Quantum Control
• Quantum approximate optimization algorithm for qudit systems
• Robust quantum gates for stochastic time-varying noise
• Maximal entropy approach for quantum state tomography
• Algorithm for the solution of the Dirac equation on digital quantum computers
• Optimised fast gates for quantum computing with trapped ions
• Single-qubit gates with errors at the $10^{-7}$ level
• Quantum error correction failure distributions: comparison of coherent and stochastic error models
• Many-Body Open Quantum Systems
• Ab Initio Molecular Dynamics on Quantum Computers
• Quantum state engineering by shortcuts-to-adiabaticity in interacting spin-boson systems
• Analytically parameterized solutions for robust quantum control using smooth pulses
• Spin transfer torque induced paramagnetic resonance
• Universal Composite Pulses for Efficient Population Inversion with an Arbitrary Excitation Profile
• Persistent dark states in anisotropic central spin models
• Dynamics of entanglement of two electron spins interacting with nuclear spin baths in quantum dots
• Numerical Methods for Detecting Symmetries and Commutant Algebras
• Dynamical and quantum effects of collective dissipation in optomechanical systems
• Continuous quantum error correction for evolution under time-dependent Hamiltonians
• Robustness of quantum algorithms against coherent control errors
• Quantum Coarse-Graining, Symmetries and Reducibility of Dynamics
• Strong-coupling emergence of dark states in XX central spin models
• Convergence of reconstructed density matrix to a pure state using maximal entropy approach
• Measurement-Based Time Evolution for Quantum Simulation of Fermionic Systems
• Taming quantum systems: A tutorial for using shortcuts-to-adiabaticity, quantum optimal control, and reinforcement learning
• Exact out-of-equilibrium central spin dynamics from integrability
• Variational Approach to Quantum State Tomography based on Maximal Entropy Formalism
• Quenched decoherence in qubit dynamics due to strong amplitude-damping noise
• Robust Quantum Control via Multipath Interference for Thousandfold Phase Amplification in a Resonant Atom Interferometer
• Photoassociation of ultracold long-range polyatomic molecules
• Angle-robust Two-Qubit Gates in a Linear Ion Crystal
• Unravelling Metastable Markovian Open Quantum Systems
• Designing dynamically corrected gates robust to multiple noise sources using geometric space curves
• Adaptive variational low-rank dynamics for open quantum systems
• Quantum Computing for Atomic and Molecular Resonances
• Non-Adiabatic Quantum Dynamics of Grover's Adiabatic Search Algorithm
• Amount of quantum coherence needed for measurement incompatibility
• Relaxation and decoherence of qubits encoded in collective states of engineered magnetic structures
• Using Spectral Graph Theory to Map Qubits onto Connectivity-Limited Devices
• Scalable quantum computation with fast gates in two-dimensional microtrap arrays of trapped ions
• Non-perturbative Floquet engineering of the toric-code Hamiltonian and its ground state
• Statistical Approach to Quantum Phase Estimation
• Characterization of quantum states based on creation complexity
• Hamiltonian learning from time dynamics using variational algorithms
• Coherent collisional decoherence
• Nonrigidity effects -- a missing puzzle piece in the description of low-energy anisotropic molecular collisions
• Generalized Hamiltonian to describe imperfections in ion-light interaction
• Dark-state photonic entanglement filters
• Engineering tunable decoherence-free subspaces with collective atom-cavity interactions
• Efficient state initialization by a quantum spectral filtering algorithm
• Quantum error pre-compensation for quantum noisy channels
• Full-Dimensional Schrödinger Wavefunction Calculations using Tensors and Quantum Computers: the Cartesian component-separated approach
• Optimal encoding of two dissipative interacting qubits
• Vibrational ladder-descending photostabilization of a weakly bound molecule: Quantum optimal control with a genetic algorithm
• Local gradient optimization of leakage-suppressing entangling sequences
• Context aware quantum simulation of a matrix stored in quantum memory
• Exact Entanglement Dynamics of Two Spins in Finite Baths
• Error correction with orbital angular momentum of multiple photons propagating in a turbulent atmosphere
• Universal set of Dynamically Protected Gates for Bipartite Qubit Networks II: Soft Pulse Implementation of the [[5,1,3]] Quantum Error Correcting Code
• Construction of Arbitrary Robust One-Qubit Operations Using Planar Geometry
• Walking with the atoms in a chemical bond : A perspective using quantum phase transition
• The quantum condition space
• Dynamics of qudit gates and effects of spectator modes on optimal control pulses
• Hybrid quantum gap estimation algorithm using a filtered time series
• Recovery of resources through sequential noisy measurements
• How pure can we go with adiabatic state manipulation?
• Electronic Structure Calculatins and the Ising Machine
• Universal Dephasing Noise Injection via Schrodinger Wave Autoregressive Moving Average Models
• Moments of Quantum Channel Ensembles
• Coherent dynamical control of quantum processes
• Overcoming the challenges in controlled thermal deposition of organic diradicals
• Quantum State Preparation and Non-Unitary Evolution with Diagonal Operators
• Electronic Structure Calculations and the Ising Hamiltonian
• Nonlinear quantum error correction